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What Is the Prisoner's Dilemma?

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Suppose that you and an accomplice are caught in the act of committing a crime. The police take you to jail and separate the two of you for questioning. In the process, the police realize that while there is enough evidence to convict both of you on charges of a lesser crime such as trespassing, without a confession there is not enough evidence to convict either of you for burglary. They separately offer you and your accomplice the following deal:

  • If both remain silent, you will both be held for one month on charges of burglary.
  • If you turn against your partner and testify while he remains silent you go free immediately while he stays in jail for a year.
  • If your partner turns against you and testifies while you remain silent, your partner will go free and you will stay in jail for a year.
  • If you both testify against each other, you will both serve a term in jail of two months.
Take a moment and ask yourself what would you do in this situation?

Prisoner’s Dilemma Explained

The above situation is the classic formulation of the prisoner’s dilemma. What did you decide to do? Remember that this offer is given independently to you accomplice. There is no way for you to know what he decides to do before you make up your mind on what your course of action will be.

The assumption is that you and your accomplice are rational. You want to have the shortest prison sentence possible. Since you cannot know what your accomplice will do, analyze the possibilities:

  • If you are silent and he is silent, then you will be in jail for a month.
  • If you betray him and he is silent, then you will spent no time in jail.
  • If you are silent and he betrays you, then you will be in jail for a year.
  • If you betray him and he is silent, then you will be in jail for two months.

Regardless of what your accomplice does, the rational choice is for you to betray your partner. The reason for this goes as follows. Suppose that he chooses to be silent. No jail is better than a month in jail, so you would betray him and testify. Now suppose that he chooses to betray you. Two months in jail is better than a year, so you would betray him and testify.

The Result

Your partner is a rational person as well and can reason in a similar way above. So he will choose the same option of betraying you. The result is that you will both serve two months in jail, an outcome that is among the worst for both of you. By working in a rational manner, you end up with a worse result than had you cooperated with one another.

Analysis

In practice, people do not act rationally when confronted with a game such as the prisoner’s dilemma. Certain levels of trust are present in society, and people can cooperate to achieve a better result than if they just acted in their own self-interest.

However the prisoner’s dilemma and analogous games do have their place in explaining behavior and phenomena in a variety of areas:

  • In psychology addiction can be modeled as a prisoner’s dilemma between a patient and his or her future self. Relapsing into addiction is similar to betrayal in the above scenario.
  • In economics many examples of the prisoner’s dilemma show up. One of them has to do with the operation of a cartel. Each member of the cartel could keep the price of an item at an agreed upon level, or one member could defect and sell at a lower price – temporarily driving up profits for itself, but causing others to defect as well. Ultimately the price would be lowered and profits would be lowered for everyone.

History of the Prisoner’s Dilemma

The prisoner’s dilemma was first formulated at RAND by Flood and Dresher in 1950. It was and still is a helpful model in analyzing the cooperation of various people or groups.

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